Problem: Solve for $s$. $0.5s+1=7+4.5s$ $s =$
Explanation: We need to manipulate the equation to get $ s $ by itself. $\begin{aligned} 0.5s+1&=7+4.5s \\\\ 0.5s+1 {-4.5s} &= 7+4.5s{-4.5s} &&\gray{\text{Subtract 4.5s from each side.}}\\\\ -4s+1&=7 &&\gray{\text{Combine like terms.}}\\\\ -4s+1{-1} &= 7{-1} &&\gray{\text{Subtract 1 from each side.}}\\\\ -4s &=6 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{-4s}{{-4}} &= \dfrac{6}{{-4}} &&\gray{\text{Divide each side by -4}.}\\\\ s &= {-1.5} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $s = { -1.5 }~~~~~~~~$ [Let's check our work!]